I had the same problem today with the software manager icon on the Mint Elyssa menu doing nothing. Software Manager would not launch. I subsequently discovered that "Mint Install", in synaptic had been marked for upgrade, but applying the upgrade was unsuccessfull. A message resulted saying that 2 of the packages could not be downloaded. I then found my way to http://packages.linuxmint.com/
and downloaded Mint Install to my desktop. Clicking on this, I was able to re-install the current version which FIXED SOFTWARE MANAGER. I fully expect however. that the next system update will break it again. Something is wrong with Synaptic's install of this program.
Key words: SOFTWARE MANAGER LAUNCH BROKEN MINT MENU ELYSSA